Implicature

“Implicature” denotes either (i) the act of meaning or
implying one thing by saying something else, or (ii) the object of
that act. Implicatures can be part of sentence meaning or dependent
on conversational context, and can be conventional (in different
senses) or unconventional. Figures of speech such as metaphor, irony,
and understatement provide familiar examples. Implicature serves a
variety of goals beyond communication: maintaining good social
relations, misleading without lying, style, and verbal efficiency.
Knowledge of common forms of implicature is acquired along with one's
native language at an early age. Conversational implicatures have
become one of the principal subjects of pragmatics. An important
conceptual and methodological issue in semantics is how to distinguish
senses and entailments from conventional conversational implicatures.
A related issue is the degree to which sentence meaning determines
what is said. Implicature has been invoked for a variety of purposes,
from defending controversial semantic claims in philosophy to
explaining lexical gaps in linguistics. H. P. Grice, who coined the
term “implicature,” and classified the phenomenon,
developed an influential theory to explain and predict conversational
implicatures, and describe how they arise and are understood. The
Cooperative Principle and associated maxims play a central
role. Neo-Gricean theories have modified Grice's principles to some
extent, and Relevance theories replace them with a principle of
communicative efficiency. The problems for such principle-based
theories include overgeneration, lack of determinacy, clashes, and the
fact that speakers often have other goals. An alternative approach
emphasizes that implicatures can be explained and predicted in all the
ways intentions and conventions can be.

H. P. Grice (1913–1988) was the first to systematically study
cases in which what a speaker means differs from what the
sentence used by the speaker means. Consider the following
dialogue.

Alan: Are you going to Paul's party?
Barb: I have to work.

If this was a typical exchange, Barb meant that she is not going to
Paul's party. But the sentence she uttered does not mean that she is
not going to Paul's party. Hence Barb did not say that she is
not going, she implied it. Grice introduced the technical
terms implicate and implicature for the case in which
what the speaker said is distinct from what the speaker thereby meant or
implied.[1]
Thus Barb implicated that she is not going; that she is not going was
her implicature. Implicating is what Searle (1975: 265–6) called
an indirect speech act. Barb performed one speech act
(meaning that she is not going) by performing another (saying
that she has to work).

By “saying,” Grice meant not the mere utterance of words,
but saying that something is the case, an illocutionary speech act
like stating but more general. What Barb said is that she has to work,
something she could have said by uttering different words. As Grice
realized, “say” is used more or less
strictly.[2]
Thus if Carl says “The largest planet is a gas giant,” we will
sometimes count him as saying (and thus not implicating) that Jupiter
is a gas giant. We will follow Grice in using “say” more
narrowly, requiring that what a speaker says be something that the
sentence uttered conventionally means (except when an indexical or
ellipsis is used). So we will take Carl to have implicated that
Jupiter is a gas giant by saying that the largest planet is.
Stating or asserting that p entails both saying and
meaning that p.

It is not possible to fully understand speakers without knowing what
they have implicated as well as what they have said. Unless we know
what Barb meant by saying that she has to work, for example, we will
not know that she has answered Alan's question. The difference
between saying and implicating also affects how we evaluate speakers.
For one thing, it determines whether meaning something one does not
believe is a lie. If Barb knew she did not have to work, then she was
lying in dialogue (1). If she knew she was going to Paul's party, she
might be guilty of misleading Alan, but not of lying. In court,
witnesses are typically required to answer questions directly.

What someone has implicated is not given to us directly. We have to
infer it from evidence. We would typically infer that Barb
meant she is not going to the party in (1) from what she said, what
Alan asked, and our assumption that Barb was responding to Alan's
question. Alternatively, we may have asked Barb whether she meant she
is not going, and inferred that she did from her answer
“Yes.” Because implicatures have to be inferred, they can
be characterized as inferences. But implicating is not itself
inferring. Hearers infer what speakers implicate. Furthermore, all
speech acts have to be inferred from contextual evidence, including
what was said and what sentence was uttered. Barb even had to infer
which person Alan was referring to.

Our sample implicature is said to be conversational. The
implicature is not part of the conventional meaning of the sentence
uttered, but depends on features of the conversational context. A key
feature was the question Alan asked. Had he asked “What are you
going to do today?”, Barb could have implicated something
completely different—“I am going to work”—by
saying the same thing. Grice contrasted a conversational implicature
with a conventional implicature, by which he meant one that is
part of the meaning of the sentence
used.[3]

(a) Jill is English and therefore brave.
(b) Jill is English and brave.
(c) Jill's being brave follows from her being English.

Speakers who use (2a) with its literal English meaning implicate
(2c). They imply, but do not say, that Jill's being brave follows from
her being English. Whereas Barb's sentence in (1) can be used
literally with its conventional meaning without implicating what she
did, (2a) cannot be used literally with its conventional meaning
without implicating (2c). In this respect, (2a) contrasts markedly
with (2b), which would rarely if ever be used to implicate (2c). The
meaning of “therefore” generates the implicature of (2a).
While Grice's examples were generated lexically, other conventional
implicatures are generated syntactically (see Potts 2005; 2007: 668).
Appositive constructions are one source: Speakers who say “Ravel,
a Spaniard, wrote music reminiscent of Spain” implicate that
Ravel was a Spaniard—they imply, but do not say, that Ravel was
a Spaniard. Hence their utterance is misleading but not a lie if they
know that Ravel was French. The implicature is conventional because
the sentence cannot be used with its English meaning without
implicating that Ravel was a Spaniard.

Bach (1999; 2006: §10) has argued against classifying (2c) (or
anything else) as a conventional implicature on the grounds
that saying that Jill is English and therefore brave is more
than saying that Jill is English and brave. Consequently
(2b) may be assertible when (2a) is not. It is even doubtful that
they have the same truth conditions. The facts Bach cites show that
Grice (1961: §3) and Levinson (1983: 128) never should have said
that the implicature of (2a) is
“detachable”—separable from what is said. The
implicature of (2a) is part of its meaning, differentiating its
meaning from that of (2b). Nonetheless, (2c) is an implicature of
(2a): (i) the speaker means that Jill's being brave follows from her
being English by saying (2a); (ii) the speaker does not say that
Jill's being brave follows from her being English. One thing that
makes this phenomenon so distinctive is that meaning (2c) is part of
meaning (2a) even though what (2c) means is not part of what (2a)
means. Hence the use of (2a) while disbelieving (2c) would be
misleading, but not a lie.

Conventional implicatures are as much inferences as conversational
implicatures. We have to infer that a speaker implicates (2c) from
the fact that the speaker uttered (2a) and is using English, together
with our knowledge of what “therefore” means in English.
We also need to know that (2a) is being used literally. A speaker who
utters (2a) ironically does not implicate (2c). Meaning (2c) is part
of meaning, not saying, (2c).

While Grice used “conventional” to denote an implicature
that is part of the linguistic meaning of a sentence, even
conversational implicatures can be conventional in the non-technical
sense in which it is conventional for women to wear a sari in India
but not Mongolia, and conventional in some languages but not others to
begin interrogative sentences with an inverted question
mark. Conventions in this sense are common practices that serve a
social interest and perpetuate themselves in a certain
way.[4]
Consider:

(a) Some athletes smoke
(b) Not all athletes smoke.

It would be unconventional (unusual, idiosyncratic, even
unprecedented) for people who say “Some athletes smoke” to
conversationally implicate that some physically fit people will
develop bladder cancer, but conventional (customary, normal, standard
practice) for them to implicate that not all athletes smoke. The
customary implicature is not conventional in Grice's sense. For
“Not all athletes smoke” is not part of the meaning of
“Some athletes smoke.” Hence there is no contradiction in
saying “Some athletes smoke; indeed, all do.” To avoid
confusion, I will describe implicatures that are conventional in
Grice's narrow sense as semantic; “conventional”
will always have the broader sense in which some conversational
implicatures are conventional too. Grice (1975: 37ff) called
conventional conversational implicatures generalized
implicatures (see also Levinson 2000).

If an implicature is conventional in either sense, we may say that
the sentence carries that implicature. Even though Barb
implicates that she is not going to Paul's party, “I have to
work” does not itself implicate this. But “Some athletes
smoke” implicates that not all do even though speakers can use
the sentence without implicating
this.[5]
(Analogy: “plane” means
“airplane” even though speakers can use
“plane” without meaning “airplane.”) As a
first approximation, a sentence has an implicature when speakers
conventionally use sentences of that form with the corresponding
implicature.[6]
Whereas knowledge of what a speaker implicates is essential to fully
understand the speaker, knowledge of what sentences implicate is a
critical component of our knowledge of a language. This is obvious
for “therefore.” But speakers are not fully competent with
“some” either unless they know that it is related to
“all” in a way that it is not related to
“several.” A man using (3a) is liable to mislead others if
he does not realize that it implicates (3b), and may fail to
communicate if he thinks it similarly implicates “It is not the
case that several athletes smoke.”

Conversational implicatures differ from semantic implicatures in
being cancelable and reinforceable. Whereas (2a)
cannot be used without implicating (2c), the indicated implicature of
(3a) can be canceled. The speaker may do this by adding “Indeed,
all do,” “and possibly all do,” or “if not
all” after uttering (3a). Or the utterance context itself may cancel the
implicature, as when it is obvious to all that the speaker is engaging
in understatement. Similarly, conjoining one sentence to a second that
means what the first merely implicates reinforces the implicature, and
does not sound redundant. Consider “Some athletes smoke, but not
all do.” This makes explicit what is normally implicit when
someone utters (3a). In contrast, conjoining (2c) to (2a) just sounds
redundant.

Grice observed that conversational implicatures are typically
connected to what is said rather than the way it is said, so that
“it is not possible to find another way of saying the same
thing, which simply lacks the implicature in question” (1975:
39). The implicature of (1) is thus said to
be nondetachable. Nondetachability would account for the
observation that the scalar implicature illustrated by (3) is
conventional not only in English but in all known languages (Horn
1989). Grice allowed exceptions to the rule, though, “where
some special feature of the substituted version is itself relevant to
the determination of an implicature” (see Grice's “maxim
of Manner” in §5). Metalinguistic implicatures —
those that refer to the particular words the speaker used — are
also clearly detachable. For example, “This is a
widgeon” may be used to convey what this species' name is in
English. A sentence with the same meaning in German has a different
implicature. We will see more detachable implicatures below.
Semantic implicatures, in contrast, are by definition non-detachable,
as we observed.

Many forms of conversational implicature occur frequently in everyday
speech and literature, with a wide variety of sentences and in all
known languages. They are common ways of both using and understanding
language. The forms are differentiated by the relationship between
what is said and what is implicated, and in some cases by the purpose
for or way in which it is implicated. Knowledge of them is an essential
component of our linguistic competence, and is acquired at an early
age. Studies have shown comprehension and production as early as age
three for metaphor and four for limiting
implicature.[7]

The most widely recognized forms of implicature are the figures of
speech (tropes). Irony, overstatement (hyperbole),
understatement (meiosis and litotes), metonymy, synecdoche, and
metaphor have been known at least since Aristotle. They are taught in
school as elements of style. When a hunter says “The weather is
lovely” ironically in a blizzard, the hunter implicates that the
weather is awful. For he means that the weather is awful by saying
that the weather is lovely. He does so to make light of the awful
weather. In the classic metonymy, the waiter says “The ham
sandwich wants more coffee,” and thereby means that the customer
who ordered a ham sandwich wants more. Figurative speech is not
literal: speakers generally do not mean what they said, and expect
their audience to recognize that. (The exception is litotes.)
Indeed, a typical clue that speech is figurative is the obvious
falsity of what is said. The hunter does not mean that the weather is
lovely, and the waiter is not expressing the belief (as opposed to the
thought) that a sandwich has desires. As a result, they do
not imply what they
implicate.[8]
Figures of speech also tend to be marked
intonationally (metonymy is an exception). They are typically used to
make speech lively, interesting, and stylish.

One figure of speech identified only recently, principally through the
work of Horn (1985; 1989),[9]
involves an irregular use of negation. The
examplar is “The glass isn't half full, it's half empty,”
but this has become an idiom applied not just to glasses. A live
example is:

A: Midori's performance was somewhat flawed.
B: Her performance was not somewhat flawed, it was nearly flawless!

In a typical use, B does not mean what the first clause says: that the
performance had no flaws. What B is trying to convey is that the
negative evaluation generally implicated by saying “It is
somewhat flawed” rather than “It is nearly flawless”
is mistaken. Irregular negations resemble irony in being marked
intonationally (“somewhat flawed” would have a normal
falling intonation in A's utterance, a fall-rise intonation in
B's).

Other general forms of implicature have become widely recognized only
since Grice (1975), including relevance implicatures, limiting
(quantity, scalar) implicatures, strengthening implicatures, ignorance
implicatures, damning with faint praise, and loose use. I call these
“modes of speech.” (1) is a relevance
implicature: the speaker implicates an answer to an expressed or
implied question by stating something related to it by implication or
explanation. (3b) is a limiting implicature: the speaker
implicates the denial of a proposition stronger than the one asserted.
Like irregular negations, these forms of implicature are not taught in
school, and names for them are not in the lexicon of typical speakers
(except “damning with faint praise” and “loosely
speaking”). Nevertheless, they are as frequent and natural as
figurative speech, and learned at the same time. Modes of speech are
not marked intonationally, and the speech is literal. They are not
used to make speech or writing lively. Speakers do not intend what
they say to be obviously false, and with one exception (loose use), do
mean what they say and imply what they mean.

The figures and modes of speech are common, socially useful practices.
They perpetuate themselves through precedent following, social
acceptance, individual habit and association, and traditional
transmission from one generation of speakers to another. Precedent
operates when hearers call on their knowledge of the forms speakers
commonly use to interpret speakers in new contexts, and when speakers
rely on that knowledge when they use the forms and expect to be
understood. The forms are less arbitrary than lexical or syntactic
conventions, but there are alternatives. No one has to implicate
rather than say things, or use the implicatures we have identified
rather than others. Alternative forms of implicature are possible and
could well have become common. For example, Some S are P
could have been used to implicate I know whether all S are
P (“knowledge implicature”) or God is to be
praised that some S are P (“praise implicature”). So
the general forms of implicature are pragmatic conventions that
complement the semantic and syntactic conventions defining particular
languages. Since the forms can be used to mean things by using a
sentence that it is not commonly used to mean, they are conventional
ways of being unconventional.

As our examples make clear, semantics, conceived as the study
of the meaning of words and sentences, does not exhaust the study of
meaning. The study of speaker meaning and implicature is included
in pragmatics, which covers the broad range of speech acts
that can be performed by using words, and properties of words and
sentences other than meaning, reference, and truth conditions. The
field of
applied pragmatics has developed out of the recognition that
second language learners cannot become fully proficient without
mastering more than grammar and literal meaning (Kasper 2003). The
phenomenon of semantic implicature (Gricean conventional implicature)
shows further that standard truth conditional semantics does not
exhaust semantics. For example, when sentences of the form
“p but q” and “p
and q” both have truth values, they have the same truth
value. Nevertheless, they differ markedly in meaning. The meaning of
“but” includes the implicature that it may be unexpected
or surprising to say that q after having said that
p. The falsity of this implicature does not make
“p but q” false. It should not be
inferred that an implicature is never entailed by what is said,
although many do (see e.g., Grice 1975: 39; Huang 2007: 56; but
contrast Bach 2006). When a speaker gives an affirmative answer to
“Did you drive somewhere yesterday?” by saying “I
drove to Ithaca,” for example, what is implicated (“I
drove somewhere”) is entailed by what is said (“I drove to
Ithaca”).

Implicature is important even in truth conditional semantics. For
example, logicians customarily take English sentences of the form
“p or q” to be true provided
“p” or “q” or both
are true. Thus “It is not the case that cats meow or purr”
would be counted as false. But there are also cases in which speakers
use “p or q” to mean that
“p” or “q” is true but
not both. Some maintain that “or” is
ambiguous in English, with an inclusive and an exclusive
sense. But another possibility is that the exclusive interpretation is
a conventional conversational implicature rather than a second sense.
One piece of evidence supporting the implicature hypothesis is that
the exclusive interpretation seems cancelable. Thus “Bill will
visit France or Germany this summer; indeed, he will drive through
both countries on his way to Poland” has no interpretation on
which it is contradictory. Another is that “Bill hopes he will
not visit France or Germany” has no interpretation on which it
ascribes to Bill a hope that would be fulfilled if he visits both
places. A methodological issue is to describe the evidence that would
be needed to decide whether a particular interpretation is a sense or
a conventional conversational implicature. A foundational issue to is
describe exactly what the difference between the two consists in.

Sentences of the form “The F is G”
imply in a distinctive way that there is one and only one F.
Russell (1905) proposed that “The F is G”
is equivalent to “There is one and only one F and it is
G.” Strawson (1950) objected that this made a statement
like “The present king of France is bald” clearly false. In
an intuitive sense, the statement presupposes rather than
asserts that there is a unique king of France. Since this
presupposition is false, the statement is out of place, and should be
withdrawn. Following Frege (1892), Strawson defined a presupposition
as a necessary condition for a statement being either true or false.
“The present king of France is bald” has no truth value,
according to Strawson, because there is no king of France. Strawson's
view thus complicates logical theory by denying bivalence. A third
position, advocated by Kartunnen & Peters (1979), is that the
uniqueness implication is a semantic implicature carried by the
definite description
construction.[10]
This allows them to maintain that “The
F is G” has the Russellian truth conditions,
while acknowledging that it is not synonymous with “There is one
and only one F and it is G.” They can allow
that the non-truth conditional component of meaning makes it as
inappropriate for us to say that “The present king of France is
bald” is false as it is for us to say that “Hillary Clinton
is a woman but smart” is true. To make matters even more complex,
the existence and uniqueness implications of negations of “The
F is G” have signal properties of
conversational implicatures, as Grice (1981) noted. Thus “The
present king of France did not visit Washington” ordinarily
presupposes that there is a present king of France. But this
presupposition is cancelled in “Since there is no such person,
the king of France did not visit Washington.”

Implicature continues to be invoked in this way to defend
controversial semantic claims:

Knowledge. The standard of
justification necessary to make a knowledge claim varies markedly from
context to context depending on what is at stake and what possibilities
are salient. On contextualist theories, sentences of the form
“S knows p” are indexical, with different
truth conditions in different contexts (Cohen 1986, Lewis
1996, DeRose 2009). An alternative theory is that sentences of this
form have a strict invariant semantics, but are used loosely to
implicate that S is close enough to knowing for the purposes
of the context (Davis 2007b; 2014). Another is that “S
knows p” has a weak invariant semantics but its
negation is used to implicate that contextually relevant alternatives
cannot be ruled out (Rysiew 2001, 2005; Brown 2006; Hazlett
2007).

Names. The popular Millian theory that the meaning of a
name is its referent entails that coreferential names are synonymous,
and that names without a referent are meaningless. This seems absurd
in light of names like “Superman” and “Clark
Kent.” Millians have proposed that the source of these
linguistic intuitions is a difference in implicature (Salmon 1986;
Soames 1989). On one version, “Superman can fly”
implicates that a man called “Superman” can
fly.[11]

Negation. On the regular interpretation of the
negation in (4), “some” is equivalent to
“any”, and the whole sentence is contradictory.

The boy did not eat some of the cookies, he ate all the cookies.

But there is another interpretation, marked by intonation and other
features, on which the negation in (4) denies the standard “not
all” implicature of “The boy ate some of the
cookies,” and is thus consistent (Horn 1989: 362–4;
370–5). (Emphasize some and all and give them
different pitches.) The question is how to account for the two
different interpretations of negations given that the word
“not” does not seem to be ambiguous (Geurts 1998). Horn
and Burton-Roberts (1989) propose that the marked interpretation of
(4) is an implicature, as it is in the Midori dialogue. Davis (2010)
argues that it is an idiom that evolved from a conventional
conversational implicature.

Implicature has also been used to explain lexical gaps.
Horn observed that the lexicon of a natural language has an economical
asymmetry.[12]
Logical concepts tend not to be lexicalized
if they are commonly conveyed by implicature. When “no”
appears in “___ S are P,” the result is a
sentence meaning “AllS are
not-P.” There is no English word, however, that in the
same context would produce a sentence meaning “Not allS are P.” Horn attributes this to the fact that
“Some S are P” conveys “Not all
S are P” by implicature, while no English
sentence conveys “All S are not-P” by
implicature. Similarly, there is an English word meaning “not
either” (“neither”), but no term meaning “not
both.” Horn connects this with the fact that “p or
q” implicates
“¬(p&q),” while no sentence form
implicates “¬(p∨q).” Given that
Horn's evidence is correlational, it is possible that the causation
goes the other way, however, with the implicatures filling the lexical
gaps. If there were a word “nome,” meaning “some but
not all,” it seems doubtful that “Some S
are P” would implicate “Not all S
are P.” Hearers could reason that if the speaker had
been in a position to say “Nome S
are P,” she would have. Moreover, the correlations are
imperfect. “Only someS are P”
means “Some but not all S are P,” even
though that meaning is implicated by “Some S
are P.”

In addition to identifying and classifying the phenomenon of
implicature, Grice developed a theory designed to explain and predict
conversational implicatures. He also sought to describe how such
implicatures are understood. Grice (1975: 26–30) postulated a
general Cooperative Principle and four
maxims specifying how to be cooperative. It is common
knowledge, he asserted, that people generally follow these rules for
efficient communication.

Cooperative Principle. Contribute what is
required by the accepted purpose of the conversation.

Maxim of Quality. Make your contribution true; so do not
convey what you believe false or unjustified.

Maxim of Quantity. Be as informative as required.

Maxim of Relation. Be relevant.

Maxim of Manner. Be perspicuous; so avoid obscurity and
ambiguity, and strive for brevity and order.

Grice viewed these rules not as arbitrary conventions, but as
instances of more general rules governing rational, cooperative
behavior. For example, if Jane is helping Kelly build a house, she
will hand Kelly a hammer rather than a tennis racket (relevance), more
than one nail when several are needed (quantity), straight nails rather
than bent ones (quality), and she will do all this quickly and
efficiently (manner).

Relevance implicatures like (1) are thought to arise from the
maxim of Relation. Barb would have infringed the maxim of Relation, it
is claimed, unless her contribution were relevant to the purpose of the
conversation. If Barb is being cooperative, then she is trying to
answer Alan's question. Given that working is incompatible with
partying, Barb must have intended to communicate that she is not going
to the party. Limiting implicatures like (3) are explained in terms of
the maxim of Quantity, and so are called quantity
implicatures. Assuming that the accepted purpose of the
conversation requires the speaker to say whether or not all athletes
smoke, a speaker who said “Some athletes smoke” would be
infringing the Quantity maxim if she meant only what she said. So she
must have meant more. If she believed that all athletes smoke, she
would have said so. Since she did not, she must have meant that some
but not all athletes smoke. As a bonus, she achieved brevity, in
conformity to the maxim of Manner. A precursor of this explanation can
be found in Mill (1867: 501).

Grice thought some implicatures arise by flouting maxims.
This happens when what a cooperative speaker says so patently violates
a maxim that the hearer must infer that the speaker means something
different. Irony and metaphor are thought to arise from flouting the
maxim of Quality. Thus Cindy might answer Alan ironically as
follows.

Alan: Are you going to Paul's party?
Cindy: I don't like parties.

If Alan knows full well that Cindy is a party animal, he could
reason that if she meant what she said, she would be lying, thus
violating Quality. So she must have meant something else. If she meant
that she does like parties, then she would be in conformity with the
maxim. And via Relation, she would have answered Alan's question
indirectly.

Generalizing from these examples, Grice provided a theoretical
account of conversational implicature that has
been widely adopted, sometimes with subtle variations. A representative
formulation goes as follows, with S the speaker and
H the hearer.

(i) S is presumed to be observing the Cooperative
Principle (cooperative presumption);
(ii) The supposition that S believes p is required
to make S's utterance consistent with the Cooperative
Principle (determinacy); and
(iii) S believes (or knows), and expects H to
believe that S believes, that H is able to determine
that (ii) is true (mutual
knowledge).[13]

Given this account, Barb's implicature in (1) is conversational
provided: Barb was presumed to be contributing what is required by the
accepted purpose of the conversation; the supposition that she
believes she is not going to the party is required to make her
utterance consistent with the Cooperative Principle; and she believes,
and expects Alan to believe that she believes, that Alan is able to
determine that that supposition is required. It would seem more
natural for Grice to have put “S
implicates p” in place of “S
believes p” in (ii). Indeed, this substitution is
allowed by further theoretical assumptions that Grice makes.

Grice also held that conversational implicatures could be
“calculated” using the Cooperative Principle.

Calculability Assumption: Conversational
implicatures must be capable of being worked
out.[14]

To work out an implicature is to infer it in a specific way
from the Cooperative Principle using particular facts about the meaning
of the sentence uttered and the context of utterance.

The presence of a conversational implicature must be
capable of being worked out; for even if it can in fact be intuitively
grasped, unless the intuition is replaceable by an argument, the
implicature (if present at all) will not count as a conversational
implicature; it will be a conventional implicature. To work out that a
particular conversational implicature is present, the hearer will rely
on the following data: (1) the conventional meaning of the words used,
together with the identity of any references that may be involved; (2)
the Cooperative Principle and its maxims; (3) the context, linguistic
or otherwise, of the utterance; (4) other items of background
knowledge; and (5) the fact (or supposed fact) that all relevant items
falling under the previous headings are available to both participants
and both participants know or assume this to be the case. A general
pattern for the working-out of a conversational implicature might be
given as follows: He has said that q; there is no reason to
suppose that he is not observing the maxims, or at least the
Cooperative Principle; he could not be doing this unless he thought
that p; he knows (and knows that I know that he knows) that I can see
that the supposition that he thinks that p is required; he has done
nothing to stop me thinking that p; he intends me to think, or is at
least willing to allow me to think, that p; and so he has implicated
that p.” (Grice 1975: 31; my emphasis)

Grice's Theoretical Definition entails that S's
implicating p is conversational only
if S's believing that p is required by the
Cooperative Principle, and only if
S believes that H can determine that S's
belief is required. The Calculability Assumption goes further,
entailing that H is able to reason from the fact that
S's belief is required to the conclusion that S has
implicated p. The Theoretical Definition says that an implicature is
conversational provided conditions (i)–(iii) are satisfied. It
does not entail that H can validly infer that S
implicated p from (i)–(iii). The Calculability
Assumption does that.

In addition to postulating that the conversationality of an
implicature depends on the cooperative presumption, determinacy, and
mutual knowledge conditions, and that the implicature can be recognized
on the basis of those conditions, Grice claimed that they give
riseto or generate the implicatures. The
implicatures exist because conditions (i)–(iii) are
satisfied.

Generative Assumption: Implicatures that
are conversational exist because of the fact that the cooperative
presumption, determinacy, and mutual knowledge conditions
hold.[15]

Whereas the Calculability Assumption is epistemological, the
Generative Assumption is ontological, explaining the constitution of
conversational implicatures. On Grice's view, the factors that give
rise to conversational implicatures are precisely those that enable
hearers to recognize them.

From his assumption that conversational implicatures can be
explained and predicted on the basis of facts about the Cooperative
Principle, Grice drew a methodological conclusion:

Grice's Razor: Other things equal, it is
preferable to postulate conversational implicatures rather than senses,
semantic implicatures, or semantic presuppositions because
conversational implicatures can be derived from independently motivated
psycho-social
principles.[16]

The pithy formulation is “Senses are not to be multiplied
beyond necessity,” alluding to Ockham. If a phenomenon can be
explained and predicted in terms of such principles, then it is
theoretically more economical to do so than to posit senses and the
like, which cannot be so explained. Grice's Razor is often invoked to
support classifying the exclusive interpretation of “p
or q” as an implicature rather than as a second sense.
The thought is that given the inclusive sense, it can be predicted
using the Cooperative Principle that speakers will commonly use
“p or q” to implicate that not both are
true. Griceans conclude there is no need to postulate a second sense.

While Grice viewed his ideas as tentative and exploratory, followers
have taken the theory to be well established. Indeed, it has served as
a paradigm for research in pragmatics. Seemingly insurmountable
difficulties abound, however (see Davis 1998; Lepore and Stone forthcoming).

The Generative Assumption attributes conversational implicatures in
part to the belief or assumption that a particular speaker is
observing the Cooperative Principle. What a hearer H
presumes about a speaker S is relevant to
whether Scommunicates with H.
For S communicates with H only if H
understands S. But implicatures are not necessarily
communicated. Indeed, speakers can engage in implicature without even
trying to communicate, as when they deliberately speak in a language
their audience cannot understand, or when they have no audience at
all. All the figures and modes of speech can appear in private
journals. Conversational implicatures depend on features of the
utterance context, but the utterance context is not always a
conversation. When there is no conversation, the Cooperative
Principle does not apply.

The Cooperative Principle assumes that every conversation is an
exercise in pure cooperation, in which participants strive only to
achieve common goals. From the perspective of social psychology,
evolutionary biology, and game theory, Pinker (2007) observes
that pure cooperation is generally an unrealistic idealization or
naive assumption. Conversations are often among adversaries, whose
goals are mainly if not completely opposed. It would be foolhardy for
an interrogator to presume that a prisoner of war or terrorism suspect
is observing the Cooperative Principle. Even when participants are
friends or relatives, they often have some divergent goals. To the
extent that they diverge, the speaker's goals may be promoted and the
hearer's goals thwarted by withholding information, providing
misinformation, going off on a tangent, or being obscure. Diplomats
do all these things to achieve some common goals while leaving other
matters in dispute. A further problem is that hearers may falsely
assume that a speaker is being uncooperative (Saul 2010: 171). Even
when a speaker is either not observing the Cooperative Principle or
not presumed to be observing it, the speaker may use all the figures
and modes of speech. If the prosecuting attorney asks the defendant
whether he was in the bank on the day of the robbery, the defendant
might answer “I took my mother to the hospital that day,”
thereby implicating that he was not at the bank. He may do this in
the hope of misleading the jury as well as the prosecutor. The
official purpose of the conversation is to get at the truth, the whole
truth, and nothing but the truth. But the defendant's purpose is to
hide it. The defendant and prosecutor do share one goal in this
situation, namely communication. But cooperation on that goal does
not require following any of Grice's maxims.

A problem for the Generative Assumption and Calculability is that
nothing in the cooperative presumption, determinacy, or mutual
knowledge conditions tells us that the speaker implicates p
rather than saying
p. The same information gets “contributed” either
way. (Note that “S implicates p” is
outside (i)–(iii) in the Theoretical Definition.) Furthermore,
nothing in conditions (i)–(iii) tells us
what Sintends. But as Grice (1957, 1969) himself
emphasized, what a speaker means or implies depends on the speaker's
intentions. Nothing in Grice's working out schema tells us
that S intended to express or communicate the belief
p, or get H to believe p, by
saying q. Without such intentions, it cannot be true
that S implicated
p.

Many have argued that Gricean theory
“overgenerates.”[17]
For nearly every implicature that appears
to be correctly predicted by Gricean theory, others appear to be
falsely predicted. The schema used to “work out” observed
implicatures can usually be used just as well to work out nonexistent
implicatures. So the schema as formulated is not a reliable method of
inferring implicatures. By a simple application of Mill's Methods, such
failures of differentiation would mean that the observed implicatures
do not exist because of the Gricean factors.

To illustrate the problem here, we will focus on the case that has
been most extensively studied, and is generally considered a paradigm
application of Gricean theory: the derivation of limiting implicatures
like (3) from the maxim of Quantity, according to which one is to be
just as informative as required. The idea is that if the speaker were
in a position to make the stronger statement, he would have. Since he
did not, he must believe that the stronger statement is not true.
Limiting implicatures are called scalar implicatures because
the weaker and stronger statements form a scale. Levinson's
influential formulation is the most detailed.

To show that these regular scalar inferences are indeed
implicatures we need now to produce a Gricean argument deriving the
inference…. A short version of the argument might go as follows:

The speaker has said A(e2); if
S was in a position to state that a stronger item on the scale
holds—i.e. to assert
A(e1)—then he would be in breach of
the first maxim of Quantity if he asserted
A(e2). Since I the addressee assume that
S is cooperating, and therefore will not violate the maxim of
Quantity without warning, I take it that S wishes to convey
that he is not in a position to state that the stronger item
e1 on the scale holds, and indeed knows that it
does not hold

More generally, and somewhat more explicitly:

S has said p

There is an expression q, more informative than p
(and thus q entails p), which might be desirable as a
contribution to the current purposes of the exchange (and here there is
perhaps an implicit reference to the maxim of Relevance)

q is of roughly equal brevity to p; so S
did not say p rather than q simply in order to be
brief (i.e. to conform to the maxim of Manner)

Since if S knew that q holds but nevertheless
uttered p he would be in breach of the injunction to make his
contribution as informative as is required, S must mean me,
the addressee, to infer that S knows that q is not
the case (K¬q), or at least that he does not know
that q is the case
(¬Kq).[18]

(Levinson 1983: 134–135)

In the typical case represented by (3), S says “Some
athletes smoke” (e2, p), and
implicates “Not all athletes
smoke” (¬e1, ¬q). The
stronger statement S does not make (e1,
q) is “All athletes smoke.” Countless statements
would have been more informative, however, many of which are comparably
brief. Indeed, “Some athletes smoke” is the low point on
several different scales. The seven lists below all go from weakest to strongest.

Some athletes smoke
Several athletes smoke
Many athletes smoke
Most athletes smoke
Nearly all athletes smoke
All athletes smoke

Some athletes smoke
At least 1% of athletes smoke
At least 10% of athletes smoke
At least 50% of athletes smoke
At least 90% of athletes smoke
100% of athletes smoke

Some athletes smoke
Some athletes smoke occasionally
Some athletes smoke often
Some athletes smoke regularly
Some athletes smoke constantly

Some athletes smoke
Some athletes and maids smoke
Some athletes, maids, and cops smoke

The reasoning Levinson has sketched could be repeated using any of these stronger statements, with fallacious results. For example:

S said “Some athletes smoke.”
If S were in a position to assert the stronger statement
“Only some athletes smoke” (i.e., “Some but not all
athletes smoke”) but did not, S would be in a breach of
the maxim of Quantity unless S wished to convey that it does
not hold. So S implicated that it is not the case that only
some athletes smoke.

This is the very opposite of the implicature Levinson claimed to
derive. Among the infinity of statements stronger than “Some
athletes smoke,” “All athletes smoke” is highly
unusual in that people typically implicate its
denial.[19]

Many other differences in implicature are difficult to explain in
terms of Gricean theory. Suppose H asks S “Do
any athletes smoke?” If S answered “Some
do,” S would typically implicate that not all smoke. A
logically equivalent answer, however, would be “Yes.” But
if S gave that answer, S would typically not
implicate that not all athletes smoke. A “Yes” answer
leaves it open whether or not all athletes smoke. Since a speaker who
answers a yes-no question “Yes” is being fully cooperative,
the Cooperative Principle cannot require the speaker who answers
“Some do” to provide any more information than
“Yes” provides.

Similarly, Leech (1983: 91) noted that “John met a woman”
implicates “John did not meet his wife,” and accounted for
this as a quantity implicature, using the sort of reasoning Levinson
sketched. But a parallel statement like “John supports
someone” does not implicate “John does not support
himself.”

Harnish (1976) observed that “Bill and Tom moved the
piano” commonly implicates that Bill and Tom moved the piano
together. A Levinsonian explanation in terms of Quantity
would attribute this implicature to the fact that the speaker did not
make the stronger statement that they moved the piano separately. If
this explanation were sound, we could equally well conclude that the
speaker implicated that Tom and Bill moved the
piano separately, given that the speaker also did not make
the stronger statement that they moved the piano together. Levinson
(1983: 146ff) himself recognized that the togetherness implicature
could not be explained in terms of Quantity, and suggested that
a Principle of Informativeness took precedence for some
unknown reason. That principle enjoins you to “read as much
into an utterance as is consistent with what you know about the
world.” But since the reading “Tom and Bill moved the
piano separately” satisfies this principle just as well (many
pianos have wheels enabling one person to move them),
Levinson's account also fails to differentiate.

Another problem is to explain why we often find
“close-but” implicatures rather than limiting implicatures
(Davis 1998: §2.1, §3.6). Suppose someone asks “How
did the Ethiopians do? Any gold medals?” The answer “They
won some silver medals” would implicate “They did not win
any gold medals” rather than “They did not win all silver
medals.” “They won some gold medals” is not stronger
than (i.e., does not entail) “They won some silver
medals,” while “They won all silver medals” is. The
Levinsonian derivation falsely predicts the quantity implicature and
fails to predict the close-but implicature.

Finally, stress plays a role in signaling or generating implicatures
that Gricen theorists have not addressed (cf. Van Kuppevelt
1996). With no stress, “Beethoven wrote some wonderful
music” would not ordinarily have a limiting implicature, in
contrast to “Beethoven wrote some wonderful
music.” “Beethoven wrote some wonderful
music” and “Beethoven wrote some
wonderful music” would have limiting implicatures, but
different ones. Since stress does not affect the set of stronger
statements, the Levinsonian derivation would predict the same limiting
implicatures no matter what is stressed. If the maxim of Quantity
explains why “Beethoven wrote some wonderful music”
implicates “Not all Beethoven's music is wonderful,” it
should also predict that “Beethoven wrote some wonderful
music” with no stress or different stress has the same
implicature. Accounting for the differences in implicature described
in this section is an outstanding problem for pragmatic theory.

Grice's determinacy condition states that S conversationally
implicates p only if S has to believe (and
implicate) p if S's utterance is to be consistent
with the Cooperative Principle. Determinacy is a key premise in the
working-out schema. It is hard to find contexts, though, in which the
determinacy condition is satisfied. There are normally many
alternative ways for a speaker to be cooperative, and contribute what
is required by the purpose of the conversation, even when the meanings
of the words used and the identity of any references are taken as
given.

For Grice, irony involves flouting the maxim of Quality.
Thus when Cindy (the party animal) answered Alan in (5) by saying
“I don't like parties,” he could reason that if she meant
what she said, she would be lying, and thus violating Quality. If she
meant that she loves parties, and therefore is going to Paul's party,
then she would be in conformity with the maxim. So that must be what
she meant. This reasoning, however, takes Cindy's belief that she
loves parties as given, and infers what she must have meant to be
cooperative. It was not the Cooperative Principle that required her to
believe that she loves parties. She would have made a suitable
contribution to the conversation if she had meant and believed that
she does not like parties, and consequently is not going. The
determinacy requirement is unsatisfied in the case of irony and other
figures of speech because the speaker could have been speaking
literally, believing what was said (cf. Saul 2010: 172). There is also
the possibility of using another figure of speech. For example, Cindy
would have made a suitable contribution to the conversation if she had
been engaging in understatement instead of irony, meaning and
believing that she hates parties.

The possibility of speaking figuratively also undermines the
determinacy requirement when the speaker is actually being literal. In
(1), Barb was speaking literally. But she could have been speaking
ironically, meaning and believing that she did not have to work,
thereby giving an affirmative answer to Alan's questions. In general,
whether S observes Quality, and therefore the Cooperative
Principle, depends on how what S believes relates to what
S implicates. These are independent variables. But Grice's
theory claims that what S implicates is that which the
Cooperative Principle requires S to believe, making
implicature the dependent variable. Independent of what S
means and implicates, the Cooperative Principle does not tell us what
S believes.

Metaphors are often difficult to interpret. Suppose a commentator says
“Iraq was Bush's Vietnam,” referring to George W. Bush and
the second Gulf War. Did she mean that the U.S. lost in Iraq the way
it lost in Vietnam? That the reasons for going to war in Iraq were as
misguided as those that got the U.S. into Vietnam? Or did she perhaps
mean that even though the U.S. did not secure all its objectives, the
Iraq war was still worth fighting? According to Gricean theory, what
the woman implicated is that which she has to believe to conform to
the Cooperative Principle. But in many conversations, she could mean
and believe any of these things and still be making a useful
contribution. So no one of the beliefs is required. Grice (1975:
39–40) said that “the conversational implicatum in such
cases will be a disjunction of such specific explanations; and if the
list of these is open, the implicatum will have just the kind of
indeterminacy that many implicata do in fact
have.”[20]
But if our commentator is typical, she will not have implicated the
disjunction of the possibilities suggested above. Implicating such a
disjunction would be highly unusual and contribute little to a typical
conversation. If the indeterminacy Grice perceives here is the
incalculability of the implicatum, then it contradicts the determinacy
condition.[21]

Ignorance implicatures are often an alternative to limiting
implicatures. Note a major lacuna in Levinson's attempt to
derive S implicated “Not all ...” from S said
“Some … .” The last line of his derivation was
not that scalar implicaure but rather a weaker epistemic
disjunction: S must mean “S knows that not all
…” or at least “S does not know that all
…” Indeed, S may well have implicated
either “Not all athletes smoke” or “I do not know
whether all smoke,” but is highly unlikely to have implicated
both. The fact that both alternatives could be cooperative means that
the determinacy condition is unsatisfied. S does not have to
believe that not all smoke to conform to the Cooperative
Principle. Not believing that all smoke suffices. But then Gricean
theory rules that S did not implicate that not all smoke even
in contexts in which S did.

Rysiew (2000) made the natural suggestion that the determinacy
condition be weakened, replacing “has to believe (and implicate)
p” with “is likely to believe (and implicate)
p.” As he notes, hearers commonly use abduction to
figure out what speakers have implicated (cf. Hobbs et
al. 1993). Abduction is a specific form of inductive or
non-demonstrative reasoning in which a hypothesis is inferred to be
true from the fact that it provides the best explanation of the
data. By their nature, non-demonstrative methods are not guaranteed to
succeed. This fact of life is no reason to shun abduction or other
forms of induction when seeking to discover implicatures. The goal of
the Theoretical Definition, however, is to set out necessary and
sufficient conditions for an implicature to be conversational, and the
Generative Assumption seeks to describe conditions that explain why
the implicatures exist. Elaborations of the examples given above will
show that an implicature can exist and be conversational even though
the available evidence does not make that implicature (or belief) more
likely than others.

Saul (2001, 2002) and M. S. Green (2002) have suggested that
“implicature” be defined normatively.
Alternatively, we might view determinacy as a condition for
properly implicating something. Determinacy is more plausible
as a norm, but similar considerations show that it is not required
even for properly meaning one thing by saying something else (Davis
2007a). For example, a speaker who says “I ate some of the
cookies” could properly be implicating either “I ate them
all” (engaging in understatement), or “I did not eat them
all” (using a limiting implicature), or “I do not know
whether I ate them all” (using an ignorance implicature). Yet
none of these contributions is required given that all would be
appropriate. Saul defends determinacy as follows.

Conversational implicatures are, among other things,
claims that audiences are required to assume the speaker to
believe, in order to make sense of the speaker's utterances. Because
of this they are claims that the audiences should arrive at,
but may not. (Saul 2010: 180)

As we noted above, if S has meant p in any way
then H must recognize that S meant p if H is to
fully understand S.H need not take S
to believe p; H may realize that S is
trying to mislead him. For a variety of reasons,
furthermore, H may not be in a position to fully
understand S. This would happen if S says “I
ate some of the cookies” and H cannot figure out
whether S is engaging in limiting implicature or
understatement. A more obvious case is that in which S is
speaking a language H does not understand.
Finally, H can make sense of the speaker's utterance without
correctly understanding S. The hypothesis that S
meant “I did not eat them all” may provide a coherent
explanation of S's utterance even though S actually
meant the opposite. We are often confronted with more than one
interpretation that makes sense of a classic text. Accounting for
implicatures when there are alternative ways to be cooperative is
another outstanding problem for pragmatic theory.

When the Gricean maxims conflict, there is no way to determine what
is required for conformity to the Cooperative Principle. In the case of
irony, for example, Manner clashes with Quality. When Cindy says
“I don't like parties,” we cannot interpret her as meaning
what she said because on that interpretation she would be violating
Quality. But we cannot interpret Cindy as meaning the opposite of what
she said, because on that interpretation, she would be violating
Manner. It is hardly perspicuous to use a sentence to mean the opposite
of what the sentence means. Indeed, it is hard to see how any
implicatures could be worked out on the basis of the maxims, because it
would always be more perspicuous to explicately state something rather
than implicate it. While both are included in Manner, perspicuity often
clashes with brevity.

We use irony and other figures, of course, in part because we have
conversational goals other than the efficient communication of
information. We observe not only the Cooperative Principle, but also
the Principle of Style.

Principle of Style: Be stylish, so be
beautiful, distinctive, entertaining, and interesting.

Clear and simple prose—“just the facts,
please”—can be boring, tedious and dull. We liven up our
writing with figures of speech and other devices. In the process, we
sacrifice perspicuity (violating Manner). We sometimes
“embellish” a narration to make it more interesting
(violating Quality) and delete boring or ugly details even when they
are important (violating Quantity).

The Gricean maxims often clash with the Principle of Politeness,
emphasized by Leech
(1983).[22]

Principle of Politeness: Be polite, so be
tactful, respectful, generous, praising, modest, deferential, and
sympathetic.

Speakers frequently withhold information that would be offensive or
disappointing to the hearer, violating Quantity. Speakers often
exaggerate in order to please or flatter, and utter “white
lies” in order to spare the hearer's feelings, violating Quality.
People pick “safe topics” (e.g., the weather) to stress
agreement and communicate an interest in maintaining good
relations—but violating Relation. Euphemisms avoid mentioning the
unmentionable, but in the process violate Manner and Quantity.

One common motive people have for implicating something is that it is
often perceived to be more polite than asserting it (Pinker 2007). In
case (1), Barb may have answered Alan's question indirectly rather
than directly because she thinks it is more tactful and less likely to
hurt his feelings, even if she realizes he will assume that is what
she is doing. Her desire to be tactful may have led her to mislead
Alan as to why she is not going, thereby violating the maxim of
Quality either at the level of what is said (she is lying about having
to work) or at the level of what is meant (she has to work but that is
not why she will skip the party).

Prominent linguists have sought to improve on Grice's formulation of the
conversational principles, and provide a solution to the problem of
clashes. Horn (2004: §4) replaces Quantity, Relevance, and Manner
with two interrelated
principles.[23]

Q Principle: Say as much as you can
[given R].

R Principle: Say no more than you
must [given Q].

The Q principle ‘collects the first Quantity maxim [“say
at least what is required”] along with the first two
“clarity” submaxims of manner and is systematically
exploited (as in the scalar cases discussed above) to generate
upper-bounding implicata,’ while the R principle ‘collects
the Relation maxim, the second Quantity maxim [“say no more than
is required”], and the last two submaxims of Manner, and is
exploited to induce strengthening implicata’ (Horn 2004: 13).
Since Horn believes that implicatures like (6a) are derivable from the
R-principle, he calls them “R-based implicatures.” The
assumption seems to be that there is no reason to make a stronger
statement (say more) if the extra information can be contributed by
implicature. Implicature (7b) is similarly described as
“Q-based.” The assumption is that if the speaker did not
make a stronger statement (say more), its denial was implicated.

He broke a finger.
(a) He broke a finger of his own. (“R-based implicature”)
(b) ✗He did not break a finger of his own.

He entered a house.
a) ✗He entered his own house.
b) He did not enter his own house. (“Q-based
implicature”)

Horn has clearly identified two distinct and very general patterns
of meaning and interpretation. Horn's two principles, however, provide
no reason to expect the two indicated implicatures rather than those we
do not observe. How can Q predict (7b) without predicting (6b)? If (6a)
is derivable from R, why isn't (7a)? What in R predicts (6a) rather
than other strengthenings, such as “He broke someone else's
finger”? Speakers who use (6) and (7) in the typical way, and
hearers who understand them, do not appear to have such principles in
mind in any way.

Horn sometimes describes Q and R as “antinomic forces”
(e.g., Horn 2004: 14), which would be appropriate if the bracketed
material in the formulations above were omitted. Thus interpreted,
Horn's principles would clash as often as Grice's.[24] Without having any
independent means of determining which force will “prevail”
in any given case, Horn's principles would have no predictive or
explanatory value. Horn's official formulations of the two principles
avoid clashes by adding the bracketed “given” clauses. Each
principle refers to the other. Given the way these formulations
“interact definitionally” (Horn 2004: 14), however, they
are circular, and do not succeed in specifying principles. Substituting
for “Q” and “R,” what the R principle says is
“Say no more than you must given that you say as much as you can
given that you say no more than you must given … etc. ad
infinitum.”[25]

Horn goes on to formulate what he calls the Division of
Pragmatic Labor:

Given two expressions covering the same semantic ground, a
relatively unmarked form—briefer and/or more
lexicalized—tends to be R-associated with a particular unmarked,
stereotypical meaning, use, or situation, while the use of the
periphrastic or less lexicalized expression, typically more complex or
prolix, tends to be Q-restricted to those situations outside the
stereotype, for which the unmarked expression could not have been used
appropriately. (Horn 2004: 16)

Horn illustrates this division with the contrast between (8) and
(9).

She stopped the machine.
(a) She stopped the machine in the usual way. (“R-based
implicature”)
(b) ✗She did not stop the machine in the usual way.

She got the machine to stop.
(a) ✗She stopped the machine in the usual way.
(b) She did not stop the machine in the usual way. (“Q-based
implicature”)

Horn appears to be assuming, plausibly, that “stopped” and
“got to stop” have the same meaning. If so, then it is
especially difficult to see how either implicature could be derived
from Q or R, since they refer to what is said, not
how it is said. (Recall Grice's nondetachability criterion.)
Levinson (2000: 136–7) therefore reinstated a version of
Manner.[26]

M Principle: Indicate an abnormal,
nonstereotypical situation by using marked expressions that contrast
with those you would use to describe the corresponding normal,
stereotypical situation.

Levinson takes this to imply that (9) implicates (9c): She stopped
the machine in an unusual way, which he describes as an M
implicature; it is also an R implicature. Horn's Q-based implicature
(9b) is equivalent to (9c) given what is said in (9); and both appear
to be genuine implicatures of (9). M provides no reason, however, to
predict (6a) or (7b).

When we look at clear cases in which a single word is synonymous with
a less lexicalized and longer phrase, we often find no difference in
implicature (e.g., mare versus adult female
horse). And the word often connotes an unusually good example of
the kind (e.g., stallion in common parlance connotes an
especially fast or dominant uncastrated adult male horse).
Similarly, stopping the pain and getting the pain to
stop do not differ in implicature even though there are typical
ways of stopping pain, while getting the bus to stop at M
Street has a specific implicature that stopping the bus at M
Street lacks (that the subject either was not driving the bus or
got it to stop in an unusual way). Finally, we find a similar contrast
between
kill and cause to die even though these two
expressions are not synonymous. Horn's formulation of the division of
labor as a tendency allows for such exceptions, but they are problems
for Levinson's M principle if it is to have predictive or explanatory
force.

Levinson's (2000: 76, 114) versions of Q and R have the
same circularity as
Horn's.[27]
Even though this deprives the principles
of content altogether, Levinson sought to avoid clashes by stating an
order of precedence: Q > M > R. Such an ordering would make sense
if the bracketed clauses were omitted. But then it is hard to see why
(6) should have an R implicature rather than a Q implicature. Huang
(2007: 40) reverses the ordering, saying that “the R-principle
generally takes precedence until the use of a contrastive linguistic
form induces a Q-implicature to the non-applicability of the pertinent
R-implicature….” This makes it hard to explain why (7) has a Q
implicature, or how (9) could have both a Q and an R implicature.

Bidirectional Optimality Theory (BOT) is another way of replacing
Grice's Quantity, Relevance, and Manner (Blutner 2000,
2004).[28] This
is a formal framework with many applications. Dekker & van Rooy
(2000) show how BOT can be modeled in game theory, with optimality
being a Nash equilibrium. BOT can be applied to the problem of
predicting and explaining what is implicated on the basis of what is
said via an appropriate Optimality Principle. One can be stated
without introducing new technical tools as follows.

Optimality Principle: Given that
S says Σ/E in C, S
implicates I iff (i) E&I is the strongest
possible contribution that is no stronger than required by the purposes
of C; (ii) there was no better way to convey E&I
than Σ.

“Σ” is the sentence S utters in
C, and “E” is what S thereby
said. The optimality is bidirectional in that condition (i) defines
“comprehension/hearer optimality” and (ii)
“production/speaker optimality.” Condition (i) combines Q
and R in a way that avoids both clashes and circularity, while (ii)
replaces M and Manner, plus possibly Politeness and
Style.[29]
To
illustrate how Optimality works, consider a limiting implicature such
as (3). The speaker utters “Some athletes smoke”
(Σ) and thereby asserts “At least some athletes
smoke” (E). Consider three alternatives: S
implicates “Not all athletes smoke”
(I1), “All athletes smoke”
(I2), or nothing (I∅).
The idea is that I∅ can be ruled out on the
grounds that I1 and I2
contribute more. I2 can be ruled out on the grounds
that there would have been a better way of conveying
E&I2, by uttering “All athletes
smoke.” Hence S implicated I1.

One problem with this account of scalar implicature is that without
knowing something about S's context C, there is no
basis for the claim that E&I∅ does not
suffice for the purposes of C. The Optimality Principle might
account for particularized but not generalized implicatures. It is also
not evident why “Only some athletes smoke” wasn't a better
way to convey E&I1, blocking the conclusion
that S implicated “Not all athletes smoke.” Why
doesn't the increase in clarity/explicitness outweigh the marginal
increase in sentence length?

When Optimality is applied to examples (8) and (9), these problems
are magnified. In typical contexts, why would someone who used either
sentence to assert that a man stopped the machine in some way
be required to contribute anything more to the conversation? And
without already knowing what these sentences implicate, how can we
determine which sentence provides the better way of conveying that the
man stopped the machine in a usual or unusual
way?[30]

The most influential alternative to Gricean and neo-Gricean theory,
called “Relevance Theory,” was developed by Sperber and
Wilson.[31]

We have proposed a definition of relevance and suggested
what factors might be involved in assessments of degrees of relevance.
We have also argued that all Grice's maxims can be replaced by a single
principle of relevance—that the speaker tries to be as relevant
as possible in the circumstances—which, when suitably elaborated,
can handle the full range of data that Grice's maxims were designed to
explain. (Wilson & Sperber 1986: 381).

“Relevance” is given a highly technical sense, roughly
meaning communicative efficiency. “The relevance of a
proposition increases with the number of contextual implications it
yields and decreases as the amount of processing needed to obtain them
increases” (Wilson & Sperber 1986: 382). Later formulations
replace “contextual implication” with the more general
notion of a “contextual effect”—roughly, what a
proposition adds to the representation of the world that is already
given in the context. These remarks suggest that a speaker does a
cost-benefit analysis, examining alternative propositions, evaluating
the number of contextual effects per unit processing cost for each,
and choosing to convey the proposition with the highest ratio. Putting
this in the style of Grice's principles yields:

Principle of Maximal Relevance (Communicative
Efficiency): Contribute that which has the maximum ratio of
contextual effects to processing
cost.[32]

Wilson & Sperber (2004: 609) illustrate by imagining a speaker
whose choices are confined to the alternatives in (10).

(a) We are serving chicken.
(b) We are serving meat.
(c) We are serving chicken or (72 − 3) is not 46.

They conclude that (10a) would be maximally relevant. For it entails
everything (10b) does and more, while being as easy to process. (10c)
has the same contextual effects as (10a), but is harder to process.

While Grice's maxims enjoin the speaker to communicate efficiently,
they do not require maximization. Conversely, the Principle of Maximal
Relevance does not imply Grice's principles. Nothing guarantees that
the contribution with the greatest number of contextual effects per
unit processing cost is: required by the accepted purpose of the
conversation; true or justified, and thus informative; germane to the
topic of the conversation (relevant in the ordinary sense); or
perspicuous and brief (lengthy formulations are permitted as long as
they have enough implications).

Relevance theorists have presented a wealth of valuable data, and
pointed out the inability of Gricean theory to account for it
adequately. Their theory, however, has similar deficiencies. The
Principle of Maximal Relevance clashes with the Principle of Politeness
as badly as the Cooperative Principle does. Imagine parents deciding
what to say after listening to their daughter struggle through her
clarinet recital. “Your performance was horrendous” seems
at least as easy to process as “Your performance wasn't
perfect.” And the former implies more than the latter in any
context. So “Your performance was horrendous” would seem to
have the greater ratio of contextual effects to processing cost in any
ordinary context. But considerations of their child's feelings, among
other things, will lead most parents to prefer the less efficient
contribution.[33]
Nothing in the Sperber and Wilson theory, furthermore, accounts for why a
speaker would say “Some athletes smoke” and implicate
“Not all do” rather than vice versa. This choice is a
matter of style and emphasis rather than informativeness or
effort.

A separate problem is that anything a speaker might say or implicate
other than logical truths will have an infinitely large set of
contextual effects. And we have no way of measuring processing
cost—not even a unit. So “the maximum ratio of contextual
effects to processing costs” is generally either undefined or
unknowable. Consequently the Principle of Maximal Relevance cannot be
used to account for specific particularized implicatures. In example
(1), for instance, there is no reason to believe that “I am not
going to Paul's party” or any other proposition would have
greater contextual effects per unit processing cost than what Barb
literally said. As for generalized implicatures, sentences of the form
“Some S are P” are used to implicate
“Not all S are P” in a wide variety of
contexts. What reason is there to think that “Not all S
are P” will have the maximum contextual effects per unit
processing cost in every one of these contexts? Many alternatives seem
more informative while just as easy to process (§7).

Sperber and Wilson sometimes formulate the Principle of Relevance in
terms of optimal relevance rather than maximal.
“An ostensive stimulus is optimally relevant to an addressee if
and only if it has enough contextual effects to be worth his attention
and puts him to no unjustified processing effort in accessing
them” (1987:
743).[34]
Being qualitative, this may avoid the
measurement problem. But calculability and determinacy go with it.
Optimal relevance so defined does not pick out a unique contribution to
the conversation. Many propositions will be informative enough to be
worth processing other than those actually implicated. In example (1)
again, “I am not going to anyone's party” would also seem
to be worth processing. Wilson & Sperber (2004: 614) argue that
there should never be more than one because “A speaker who wants
her utterance to be as easy as possible to understand should formulate
it … so that the first interpretation to satisfy the hearer's
expectation of relevance is the one she intended to convey.” But
neither optimal nor maximal relevance requires the speaker to minimize
processing cost. Additional effort can always be justified by a
proportionate increase in informativeness. We cannot simply look for
the most accessible way to convey what is being communicated, for this
theory is supposed to predict what is being communicated based solely
on considerations of efficiency.

Relevance theory reasoning also seems to overgenerate implicatures. Suppose
that in a discussion of a new prescription drug benefit, someone
comments “It will take some money to fund that program.”
The speaker would normally have engaged in understatement, implicating
“The program will be very expensive.” Relevance theorists
account for this by saying that because the proposition explicitly said
is trivial, and thus has few contextual effects, the hearer will
“recover” the more informative
proposition.[35]
But
countless propositions are more informative than the one implicated,
such as “The program will cost trillions,” and seem as easy
to process. If the reasoning were valid, moreover, we should expect all
tautological sentences to have non-tautological implicatures; but such
implicatures are the exception rather than the rule.

The analysis of example (10) given above, finally, would seem to
imply that a speaker who uttered (10b) would assert or implicate (10a),
since that is maximally relevant (cf. Carston 1988: 43). In fact, such
a strengthening (or R implicature) would be unlikely.

Given the definition of contextual effects, both Maximal and Optimal
Relevance seem to imply that speakers cannot implicate anything that is
already given in the context. For the ratio of contextual effects to
processing costs in that case must be zero. This prediction is not
borne out. If A and B are walking in torrential rain,
A might say “It is raining really hard,” stating
the obvious, and B might respond “There is indeed some
rain coming down,” engaging in understatement and implicating
exactly what A said

A final problem for either formulation is that the
body of contextual assumptions or background information, in terms of
which contextual effects are defined, is indeterminate. In example
(5), Cindy answered Alan by saying “I don't like parties,”
implicating that she is going to Paul's party. Is the fact that Cindy
loves parties part of the context, or a potential contribution to the
conversation?

As observed in §1, Grice (1975: 24) introduced the technical term
“implicature,” using it to denote either (i) the act of
meaning or implying one thing by saying something else, or (ii) the
object of that act. Grice (1975: 87ff) used the word
“say” quite strictly, requiring what a speaker says to be
closely related to what the sentence uttered means on that
occasion. Thus if Carl utters “The largest planet is a gas
giant” referring to Jupiter, Grice would describe Carl as saying
that the largest planet is a gas giant and thereby implicating that
Jupiter is. Indexicals provide cases in which what a speaker says is
not what the sentence used means. When Barb uttered “I have to
work” in (1), she said that she, Barb, has to work; but the
sentence she used does not mean “She, Barb, has to work”
even on that occasion. Ellipsis allows people to say things without
even uttering sentences. If John asks “Where did Mary
go?” and Sue answers “To the gym,” then Sue said
that Mary went to the gym. The infinitive phrase she uttered was
elliptical for a sentence meaning “Mary went to the gym“
but does not itself mean that.

Sperber and Wilson (1986a: 182–3) introduced the parallel
technical term explicature to mean what is “explicitly
communicated.” Carston (1988: 33) identified this with
“what is said, in Grice's
terms.”[36]
In this
terminology, Barb's explicature in (1) was “She (Barb) has to
work,” and her implicature was “She is not going to
Paul's party.” Carston's (1988: 40) paradigm case is
less clear.

Alice ran to the edge of the cliff.
(a) The distraught woman jumped.
(b) She jumped off the cliff.

After saying or observing that Alice ran to the edge of the cliff, a
speaker would typically use (11a) “The distraught woman
jumped” to mean that she jumped off the cliff
(11b). Given that (11a) does not itself mean this, the speaker was
implicating rather than saying that she jumped off the cliff. Note
that if the speaker knew that the woman jumped back from the edge, the
speaker could be accused of misleading the hearer but not of lying. A
speaker who used (11a) to mean that the woman jumped up to the rescue
helicopter
said the same thing while meaning something
different.

Carston (1988: 40) classifies (11b) as an explicature on the grounds
that an implicature cannot entail what is said. This assumption has
no more basis than the converse claim that an implicature cannot be
entailed by what is said (§4). The form of understatement known
as litotes is a common figure of speech in which what is implicated
entails what is said, as when a speaker says “That's not
bad” meaning “That's good,” or “Ruth hit some
home runs” meaning “Ruth hit a record number of home
runs.” Another reason Carston offers is that (11b) is what the
hearer will remember. But what is implicated is often more important
than what is said. In dialogue (1), Alan may well forget what excuse
Barb gave because he was so disappointed that she would not be at the
party. Carston's (1988: 45; 2004a: 646-8) most interesting argument
is based on embedding. She would claim that if “Alice jumped
off the cliff” were merely an implicature of “Alice
jumped,” then we should not understand (12a) and (12b) as having
the same truth conditions. Yet we would take them to be equivalent,
Carston believes. The alleged implicature seems to fall within the
scope of the logical operator, something she believes an implicature
would not
do.[37]

(a) If Alice ran to the edge of the cliff and jumped, she is
probably dead.
(b) If Alice ran to the edge of the cliff and jumped off, she is
probably dead.

A speaker who used (11a) to mean (11b) would just as naturally use
(12a) to mean (12b), and hearers would understand the speaker
accordingly. But what the speaker said does not entail
(12b). What the speaker of (12a) said would be false in circumstances
in which Alice was unlikely to jump off the cliff if she jumped.
Hearers would focus on what the speaker meant, though, which would be
true even in those circumstances. Since the speaker meant one thing
(12b) by saying something else (12a), the speaker implicates (12b).
Note that the speaker does not implicate anything by uttering the
antecedent of (12a). The speaker says something only by uttering the
whole conditional. So there is really no embedding of implicatures
when (12a) is uttered.

The relationship between (11) and (12) is special. In many other
cases in which a sentence “p” conversationally
implicates “q,” the conditional
“If p then r” does not implicate
“If p and q then r.” For
example, “If Bill got some of the problems wrong, he might have
gotten them all wrong” does not implicate ”If Bill got
some but not all of the problems wrong, he might have gotten them all
wrong.”

Another debate between the Relevance theorists and neo-Griceans concerns
numerical claims.

Peter has one child.
(a) Peter has at least one child.
(b) Peter has exactly one child.

All parties agree that a speaker can use (13) to mean either (13a) or
(13b). Horn (1972) and Levinson (2000: 87–90) further agree with
Carston that (13) itself is unambiguous. But whereas the neo-Griceans
hold that (13) means (13a) rather than (13b), Carston maintains that
(13) means neither. Both (13a) and (13b) are
“developments” or “expansions” of the logical
form of (13) on Carston's view. So the neo-Griceans hold that (13)
always explicates (13a) while sometimes implicating (13b). Carston
holds that (13) is sometimes used to explicate (13a) and sometimes
(13b); neither is an implicature. The thesis that sentence meaning
leaves open what is said to this extent is called semantic
underdetermination. While still doubting that Carston's view can
fully account for cardinals, Horn (1989: 250–1; 2010:
314–5) now concludes that they do not behave like scalars. For
example, if you know that everyone passed, you must answer “Did
some students pass?” with “Yes.” But if you know
that Peter has two children, you cannot answer “Does Peter have
one child?” without knowing whether the speaker meant “at
least” or “exactly.”Assessing this debate is
especially difficult because of the possibility that (13) actually is
ambiguous. Grice's razor (§5) is not a good reason to reject this
possibility.

Bach (1994: 160) uses “say” even more strictly than Grice,
meaning “strictly, literally, and explicitly say.” Since
the speaker of (11a) did not explicitly say that A jumped off the
cliff, Bach would deny Carston's view that (11b) is an
explicature. Bach (1994: 125–6, 140–1; 2006: 28–9)
agrees with Carston, though, in withholding the term
“implicature” when what the speaker means is an
“expansion” or “completion” of what is said.
Bach introduces the term impliciture (with “i”
rather than “a”) to cover such cases. Bach's agreement
with Carston and disagreement with Grice about what is implicated is
merely verbal, however. For Bach defines “implicature”
more narrowly than Grice, restricting it to cases in which what is
meant is “completely separate” from what is said.

A thesis associated with Grice is that what S says is
determined by “decoding,” while what S implicates
is determined by what S says together with an inferential,
pragmatic mechanism. An alleged problem for this view, called
“Grice's Circle” by Levinson (2000: 173–4,
186–7), is that many of the processes involved in figuring out
what is said, such as reference identification and ambiguity
resolution, “involve exactly those inferential mechanisms that
characterize Gricean pragmatics.” Grice never talked about
decoding however, and observed himself that conversational principles
are involved in determining what is said (Grice
1957: 222).[38]
For
example, if an ambiguous term is used, we naturally
assume—without specific counterevidence—that the intended
meaning was the one relevant to the topic of conversation. In a
discussion of snow, “There is a large bank on Main Street”
is naturally interpreted as referring to a snow bank. That recognition
of explicatures is not simply a matter of “decoding” is
proven by the simple fact that we have to infer what language or code
S is using, and what speech act S is performing,
before we can use our knowledge of the language to (help) determine
what S said. A speaker can utter English words without using
English. When Jack answered “Sugar” in response to someone
who asked in Spanish what he bought for $150 a gram, we may rely on the
maxim of Quality to help us determine that Jack is using a drug code.
Our knowledge of English will not tell us what he said, if anything.

There is no circle in Grice's view because what is said is the
conclusion of one pragmatic inference, and is one of the premises in a
further pragmatic inference to what is
implicated.[39]
The process is serial
rather than parallel, although later conclusions may always lead to
adjustment of earlier conclusions. Bach (2006: 25) claims that we need
not determine what S said before inferring what
S implicated (see also Carston 2004a: 72 and Meibauer 2006: 577). He correctly
observes that we can often determine what Smeant
before determining what S said. But by definition, we cannot
conclude that S implicated p before establishing
that S did not say p. And we cannot conclude
that S implicated p by saying q before establishing
that S said q (cf. Borg 2010:
281).[40]

If theories that seek to derive conversational implicatures from
general conversational principles all have outstanding problems, what
alternatives are there for explaining conversational implicatures, and
describing how they are understood? That depends on whether we are
concerned with speaker implicature or sentence implicature.

For a speaker to implicate something is for the speaker to mean
something by saying something else. It seems clear that what a speaker
means is determined by the speaker's intentions. When Steve
utters “Kathryn is a Russian teacher,” whether Steve means
that Kathryn is a teacher of Russian nationality or a teacher of the
Russian language, and whether he is speaking literally or ironically,
depends entirely on what Steve intends to convey. What
“convey” means precisely is a matter of considerable debate
that we can ignore
here.[41]

We most commonly explain why people do one thing A with the intention
of something something else B by explaining why they believe they will
do B by doing A, or why they want to do B. We can explain why
speakers intend to convey a thought by uttering a sentence that says
something else in the same ways. Why do speakers believe they can
convey thoughts by means of the various figures and modes of speech
identified in §3 and later sections? Because they have seen
others doing so. Knowledge of the common forms of implicature and
other forms of indirect speech is acquired along with knowledge of the
semantics and syntax of our native language. Speakers pick up figures
and modes of speech from other speakers, as they learn vocabulary and
grammar. Knowledge of both figures and modes is as tacit as our
knowledge of syntax and semantics. It is not knowledge of facts that
define a langauge, but of how a language is used and understood.
Since the figures and modes do not depend on a particular language,
they can be used with any language.

Why do speakers want to engage in implicature? The main reasons are
the reasons they make statements: to communicate, express themselves,
and record their thoughts. These goals may serve to cooperate with
others, or to oppose them. What goals are served by implicating
rather than saying something? One is verbal efficiency (Levinson
2000: 28–31; Camp 2006: 3): through implicature we express two
or more thoughts by uttering just one sentence. Another is to mislead
without lying (Horn 2010: §4). People often wish others to
believe things that are false, and not only in situations of conflict
and competition. And they nearly always prefer misleading to
lying.[42] The
greater deniability of implicature, and the fact that it enables us to
veil our intentions, are often motivating factors (Pinker 2007). We
observed earlier how implicature promotes the goals of style and
politeness. It should also be recognized that people often say and
implicate things out of habit, and sometimes do so spontaneously.

Given that speaker meaning is a matter of speaker intention, it
follows that speaker implicatures can be recognized or predicted by any
of the methods we use to infer intentions from behavior.
Suppose that while walking with us in the driving snow, Swede says
“It is a good day!” We may wonder whether he was speaking
literally, and meaning just what he said; or speaking ironically, and
meaning the opposite of what he said; or perhaps engaging in
understatement, and meaning that it is a wonderful day. We need to know
what thought Swede intended to convey. One thing we can do is ask him.
If Swede tells us that he was using irony, that would be good evidence
that he intended to convey the belief, and thus implicated, that the
weather is terrible. His intonation might be another indication. The
fact that Swede is often ironic in similar situations would be
supporting evidence. On the other hand, if we know that Swede loves
snow, and freely conveys his feelings, that evidence would make it more
likely that he intended to convey the belief, and thus implicated, that
the weather is wonderful. Finally, if Swede's companion has just
suggested that they go in because the weather is lousy, the hypothesis
that Swede intended to convey the opposite belief because he wanted to
stay out may provide the best explanation of his saying “It's a
good day.” In that case, we would infer that he meant what he
literally said.[43]

While the existence of conversational implicatures does not depend in
any way on the assumption that the speaker is observing conversational
principles, they may play a role in the recognition of
implicatures. Indeed, the Cooperative Principle and associated maxims,
along with the Principles of Style and Politeness, seem to play the
same indirect role in implicature recognition that known tendencies or
goals play in inductive inference generally. Since speakers tend to
observe the Cooperative Principle, and hearers know this in a vague
and tacit sort of way, hearers tend to assume that particular speakers
are cooperating, in the absence of evidence to the contrary. If the
hypothesis that S is implicating p fits better with
the assumption that S is being cooperative than the
hypothesis that S is not, the hearer may then conclude
that S is implicating p, by abduction. The
hypothesis may be confirmed after the fact by S's testimony.
Further support for the hypothesis may be provided by the recollection
that S and other speakers have implicated similar things in
similar circumstances before. The existence of an applicable
implicature convention would be especially powerful
evidence. Recognition of unconventional forms of implicature is more
difficult, but no more difficult than recognizing when a speaker is
using a sentence with an unconventional meaning.

When S is being uncooperative, we have to use other
generalizations. We are familiar, for example, with the ways in which
defendants manipulate language in an effort to avoid
self-incrimination. When trying to infer what such a speaker is
implicating, we use something other than Grice's working-out schema. In
general, we need to distinguish contextual clues to what a
speaker intended from contextual determinants. As is the case
with mental phenomena generally, the evidence we use to detect
implicatures is not what makes them exist.

What a speaker says is also dependent on the speaker's intentions.
Whether a speaker using “There is a large bank on Main
Street” says that there is a snow bank or a commercial bank on
Main Street depends on what the speaker means by “bank” on
that occasion. Meaning “bank” involves the intention to
convey not a belief or thought, but rather a concept. It is
unsurprising, therefore, that conversational principles play much the
same role in inferring both what is said and what is implicated
(§12).

We noted in §2 that when an implicature is conventional, we may
ascribe it to a sentence. Speakers conventionally use sentences of the form “Some
S are P” to implicate “Not all S
are P,” but not to implicate “Not more than half of all
S are
P.” Consequently “Some athletes smoke”
implicates “Not all athletes smoke” but not “Not
more than half of all athletes smoke.” Even though this
implicature is conversational, all the signs of conventionality are
present.[44]
There is
a regularity in usage and interpretation. English speakers commonly use
sentences of the form “Some S are P” to
implicate “Not all S are P,” but they
rarely if ever use them to implicate “Not more than half of all
S are
P.”[45]
Speakers are commonly understood
accordingly.[46]
These regularities are socially useful,
serving, among other things, the purpose of communication. They are as
self-perpetuating as other conventional practices. People use
“Some S are P” to implicate “Not
all S are P,” and are so understood, in part
because people have regularly done so in the past. Speakers pick up
sentence implicatures from other speakers as they learn their
language. And finally, the regularities are arbitrary to some
extent. Plenty of other practices could have served the same purpose
quite naturally, and would have perpetuated themselves in the same way
if only they had gotten started. It could have been conventional for
English speakers to use “Some S are
P” to implicate the denial of “Not more than half
of all S are P” or others listed above in the
athlete example (§7). Conversational implicature conventions are
not as arbitrary as lexical conventions, though. In all known cases,
there is some antecedent relation between what the sentence means and
the implicature that makes it natural to use one to convey the
other. But there are always alternative implicatures that would be
natural too.

There are many other limiting implicatures. For example,
“A believes p” implicates
“A does not know p,” and
“A entered a house” implicates “A
did not enter his own house.” The conventionality of sentence
implicatures is highlighted by the fact that “A
believes p” does not implicate “A
regrets p” and “A lost a book”
does not implicate “A did not lose his own book.”
Sentences also have a variety of strengthening implicatures. These
include tautology implicatures (e.g., “An N is
an N” implicates “One N is as good as
another”), conjunction implicatures (e.g., “p
and q” implicates “p
before q” or “p
because q”), and disjunction
implicatures(“p or q” implicates
“p or else q” or “p or
equivalently q”). Many sentences also carry ignorance
implicatures. Thus “Some S are P” also
implicates “I do not know whether all S
are P” and “p or q”
implicates “I do not know which of p or q is
true.”

When Grice talked about conventional implicatures he was referring
to semantic implicatures, like example (2). These
implicatures exist because of the conventions that give individual
words or syntactic structures their meanings. (2a) implicates (2c)
because it is conventional for English speakers to use
“therefore” with a certain meaning, of which the
implicature is a part. A conversational sentence implicature
is not part of the meaning of the sentence used, even when it is
conventionally used with that implicature. It is a second-order
convention: a convention to use a sentence of a given form with an
implicature that is not part of its meaning. The common modes and
figures of speech are also second-order conventions, but not
restricted to sentences with a particular form. A language is defined
by first-order lexical and syntactic conventions, not by second-order
implicature conventions. In this respect conversational implicature
conventions are like naming conventions, word formation rules,
intonation rules, speech act riturals (e.g., saying “This
is N” when answering a telephone), and indirect speech
act conventions (e.g., asking “Is it possible for me to get
an N?“ to request
an N.[47]

Like other second-order linguistic conventions, conversational
implicature conventions differ in their cross-linguistic spread.
Whereas the scalar implicature of “some” has been found in
all observed languages (Horn 1989), tautology implicatures differ
markedly from language to language (Wierzbicka 1987: 102). Thus the
literal French translation of “An N is
an N” is used without implicature, the way English
speakers use “No N is a non-N,” while
the Polish translation is used to implicate “There is something
uniquely good about an N.” The fact that regularities
in implicature obtain cross-linguistically is compatible with their
being arbitrary and conventional. The practice of using
“?” as a question mark is completely arbitrary and
conventional even though it is used in nearly all written languages.
The same goes for the use of arabic numerals for numbers. In a wide
variety of spoken languages, rising intonation is used to mark
questions, and variants of “Hello!” are used to answer the
telephone. Why some implicatures are common to more languages than
others is an open question on any view.

Many important conversational implicature conventions associate
implicatures with sentences of any form (§3). The most familiar
examples are the figures of speech. It is conventional to use a
sentence to mean the opposite (irony), or something stronger
(litotes), or something similar (metaphor). There is also a convention
whereby a sentence is used to implicate requested information by
making a statement closely related to it by implication, which gives
rise to relevance implicatures like (1). Since these conventions do
not attach implicatures to particular sentence forms, they do not give
rise to sentence implicatures.

It is plausible that conversational sentence implicatures arose in
much the same way idioms
do.[48]
“Kicked the bucket” started
life when speakers used it as a metaphor to implicate that someone
died. The metaphor caught on and became conventional. “Ground
zero” has similarly become a conventional metaphor for the focal
point of a major event or movement. Although it has not to my
knowledge been historically attested, it is plausible that the use of
“Some S are P” (or its translation in
some earlier language) to implicate “Not all
S are P” similarly started life as a nonce
implicature that caught on and spread. The difference is that with
idioms like “kicked the bucket,” the metaphor
“died,” and what previously was implied came to be meant
directly, creating a non-compositional meaning for the
expression. Consequently, idiomatic meanings have been
“detached.” The study of the origin of conversational
implicature conventions falls in the domain of historical
linguistics.

While figures and modes of speech are ways of using any sentence to
implicate, sentence implicatures are facts about particular sentences
or sentence forms. English differs from Polish, French, and Tamil in
its tautology implicatures. English today has different metaphorical
implicatures than it had just a few years ago. Knowledge of sentence
implicatures is a crucial component of the linguistic competence of
speakers and hearers (Lepore & Stone forthcoming: Part II).
Speakers who are unaware of them are likely to mislead their audience.
Imagine the possibilities if an oblivious speaker said Your
husband saw a woman to the subject's wife. Unknowing speakers
may feel compelled to say what could safely go unsaid, making their
speech long-winded. Hearers (and natural language processors) without
such knowledge are likely to either misinterpret or fail to fully
understand the speaker. Sentence implicatures, both semantic and
conversational, resemple idioms and the customary forms of speaker
implicature in being picked up by native speakers from other speakers
in the course of learning the language. Sentence implicatures thus
perpetuate themselves from one generation to the next. Recent
metaphors are special in being picked up by adults, and are liable to
become idioms if they pass on to new generations.

An impressive and growing body of research has attempted to discern
general regularities in the multitude of conversational implicature
conventions associated with a language. One set of studies, conducted
by Wierzbicka (1985; 2003), seeks to understand how implicature conventions
reflect broader “cultural scripts.” Another seeks to
describe how the implicatures of a sentence are related to the
implicatures of compound sentences in which the sentence is embedded
(Gazdar 1979; Levinson 2000: §2.5.1; Sauerland & Stateva
2007)—the question raised by example (12).

The most influential body of research on implicature conventions
describes “Horn scales,” named after Laurence Horn (1972,
1989).[49]
Horn observed that the quantifiers
all, most, many, some form a scale with the following
properties. Instances of “___ S are P”
with one term entail instances with any term to the right, but not to
the left; the terms are thus ordered by logical strength. Moreover, the
result of substituting one term implicates the denial of the result of
substituting any term to the left, but not to the right. In the context
“It is not the case that ___ S are P,”
the logical and pragmatic relations are reversed. Other Horn scales are
necessarily, actually, possibly, certainly, probably,
possibly; and must, should, may. Levinson (2000: 156)
looked for a generalization that would cover these cases but not scales
like Between 100% and 90%, at least 10%, some which have the
same logical relations as Horn scales but not the pragmatic relations.
One is that the items on a Horn scale are widely and frequently used
monolexemes (Levinson 2000: 156). This does not exclude all exceptions.
For example, “several” is monolexemic and both frequently
and widely used. It is weaker than “many” but stronger than
“some.” Yet “Some S are P”
does not implicate “It is not the case that several S
are P.” Can Levinson's generalization be refined, or is
“several” just an exception? If the generalizations are
explanatory rather than merely descriptive—that is, if they tell
us why we have some implicature conventions but not others—then
they can presumably be refined. A priori, though, there is no
more reason to expect that our conversational implicature conventions are completely
systematic than there is to expect that lexical conventions are. All
languages are “irregular” to some extent. For example, the
regular pattern for adjectives in English is that of tall, taller,
tallest. But there are exceptions, such as good, better,
best. No one expects that anything other than a historical
explanation exists for these facts.

The universality of scalar implicatures is not surprising on the
Gricean view that sentence implicatures can be derived from general
conversational principles. But the extent to which sentence
imlicatures are arbitrary and vary from language to language makes
that view untenable. Conversational principles do specify common
interests that conversational implicature conventions serve:
communication of information, politeness, style, and efficiency.
Since conventional practices sustain themselves by serving socially
useful purposes, the fact that speakers strive to be cooperative,
polite, stylish, and efficient sustains implicature conventions. We
also noted earlier that conversational principles can serve as
generalizations used in the process of inferring implicatures, and we
can add that flouting a principle often serves as a signal that an
implicature convention is in play.

The literature on implicature is enormous and growing. This entry,
regrettably, had to ignore many valuable contributions.